应用数学和力学

1993 Vol. 14, No. 11

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A Theoretical Model ol the Coherent Structure in the Wall Region of a Turbulent Boundary Layer

Luo Ji-sheng, Zhou Heng

1993, 14(11): 939-947.

Abstract(2074) PDF(497)

Abstract:
In this paper, the formation of the coherent structures in the wall region of a turbulent boundary layer was studied, using the nonlinear theory of the hydrodynamic stability. The spanwise and streamwise wavelengths of the most amplified unstable wave obtained by this study were found in good agreement with the experiments, which makes the distinct feature of this study in the present paper, as the basis of the stability analysis, a more rational velocity profile has been used, which is different from that of the turbulent mean flow. And also, the new nonlinear theory was used. The result is useful in understanding of the quasi-periodicity of the coherent structure in the turbulent boundary layer.

Contaminant Contraction in Two-dimensional Oscillatory Flows

Liu Yu-lu, Cai Shu-tang

1993, 14(11): 949-959.

Abstract(2264) PDF(534)

Abstract:
If the vertically-mixing time is comparable with that of period oscillatory current, the contaminant contraction may occur. The coefficient of shear dispersion is negative (singularity). According to the two-dimensional delay-diffusion equation derived by the author^[7]: where u(t),v(t) are vertically-averaged velocities, the equations for X(t,τ), Y(t,τ), central displacement, dispersion tensor, had been derived. D_ij is positive when τ is small. If the is large, the memory functions may be negative. Also the expressions for and X, Y had been obtained.

A Quantitative Analysis of the Travelling Wave Solution of the KdV-Burgers Equation

Lü Xian-qing

1993, 14(11): 961-966.

Abstract(1988) PDF(491)

Abstract:
By using the methods of mathematics analysis, we investigate the travelling wave solution of the KdVB equation under the assumption v²≥4μ.We prove that the travelling wave solution is quantitatively similar to the corresponding Burgers shock wave. Then we prove that the absolute error of the general asymptotic expansion is high order quantity of the small parameter ε.

influences of Body Speed on Cavitation Noise

Huang Jing-quan

1993, 14(11): 967-970.

Abstract(1651) PDF(586)

Abstract:
The present paper analyzes the relationship between the body speed and the cavitation noise. The results indicate that there is the limiting value of cavitation noise.

Nonlinear Bending of the Shallow Spherical Shells with Variable Thickness under Axisymmetricai Leads

Niu Zhong-rong

1993, 14(11): 971-978.

Abstract(1961) PDF(612)

Abstract:
Based on the differential equation of the nonlinear bending of shallow spherical shells with variable thickness under axisymmetrical loads, this paper studies the numerical solution of the nonlinear differential equation by means of interpolating matrix method. The analysis of the results indicates that the suggested method is easy to implement and obtains the same high accuracy for both the displacements and the internal forces.

A New Method for Calculating Vehicle Attitude Using Cayley-Klein Parameters

Dong Qiu-quan

1993, 14(11): 979-984.

Abstract(1631) PDF(458)

Abstract:
In this paper new matrices of the Cayley-Klein parameters are used to represent composition of several consecutive finite rotations of rigid body. The general commutative rules of multiplication for these matrices is obtained. Furthermore, by using these matrices it is convenient to prove the theorem on finite rotation of rigid body. The result obtained in this paper is concise and easy to remember, and can be used to calculate vehicle attitude.

Z_n-Equivariant Singularity Theory

He Guo-wei, Fang Tong

1993, 14(11): 985-991.

Abstract(1972) PDF(489)

Abstract:
The basic concepts, normal forms and universal unfoldings of Z_n-equivariant singularity are investigated in the present paper. As an example, the normal forms and universal unfoldings of Z₃-singularity are formulated. As a matter of fact, the theory provides a useful tool to study the subharmonic resonance bifurcation of the periodic parameter-excited system.

Control of Transpiration Cooling System and Its Characteristics

Xu Yan-hou, Yang Xue-shi

1993, 14(11): 993-1001.

Abstract(2016) PDF(702)

Abstract:
This paper gives the mathematical model of three-dimensional transpiration cooling control system in heat shield. Generally, it. a non-linear control system on variable-domain mixed up with both distributed and concentrated parameters. This paper points out that the thermal and ablative problems of the shield can be solved solely with the coolant flow only under one-dimensional incompressible or steady condition. In regard to the surface ablating problem of the thermal shield, the control schemes of the system, including its simplified condition and the characteristics of one-dimensional point control is suggested here. Solutions of the equilibrium state are given with or without phase change as far as the coolant is concerned.

Analytic Solutions of Simple Waves

Li Guo-bin

1993, 14(11): 1003-1008.

Abstract(2630) PDF(465)

Abstract:
B. Riemann furnished the general solution of simple waves in 1860^[1]. But it is difficult to find out the exact forms of the arbitrary function contained in the general solution which must satisfy boundary or initial conditions. For this reason it is inconvenient to probe into the characteristics of concrete problems. In this paper the analytic solutions of simple waves are afforded according to the geometric theory of quasi-linear partial differential equation, and they are determined with boundary or initial conditions. By using these solutions the specific properties of certain flows are discussed and novel results are obtained.

Elastostatic Solutions for Semi-Infinite Orthotropic Cantilevered Strips

Lin Yi-han

1993, 14(11): 1009-1016.

Abstract(2118) PDF(545)

Abstract:
The elastostatic solutions of semi-infinite orthotropic cantilevered strips with traction free edges and loading at infinity are governed by the differential equation Φ_1yyyy+(2+δ₀)Φ_1yyxx+Φ_1zzzz=0 with δ₀ >-4 Based on the work of [10] for δ₀>0 case,.this paper completes the case for δ₀=0 isotropic materials and the case 0>δ₀>-4 for orthotropic materials. The solutions of the above problems have important application in the properly formulated boundary conditions of plate theories for prescribed displacement edge data.

Buckling Test And Optimum Design of Fiber Reinforced Composites Plates Under Compression

Zhou zhu-lin

1993, 14(11): 1017-1024.

Abstract(1797) PDF(627)

Abstract:
In this paper,the conclusion that the experunental reschs minchk with theoretical antabsis has been for thruhyh bueklme test of comiportik mechetulur piates.It is confirned that the crithal lawck of amposine plees culculated brenuckhing theroethical fornda of anisariropic plate are reliable The nens of optinial antiem of matrix and optimal off-axis which made fover prinfroed composite photes techy biggest citthals an also discused in this paper has resit at aedlen and he used in the design for products.